Abstract
We extend the analysis on the effects of the entry constraints on the dynamics of an adaptive segregation model of Shelling’s type when the two populations involved differ in numerosity, level of tolerance toward members of the other population, and speed of reaction. The model is described by a two-dimensional piecewise smooth dynamical system in discrete time, where the entry constraints represent possible exogenous controls imposed by an authority in order to regulate the maximum number of members of the two populations allowed to enter the system, usually the district in which they live in. In this paper, we investigate the nature of some particular border collision bifurcations and discuss the policy implications of the entry constraints in terms of segregation. The investigation reveals that asymmetries in the level of tolerance of the two populations involved may lead to phenomena of overreaction or overshooting in the adjustment process. In order to avoid the risk of segregation, suitable entry limitations must be imposed at least on the more tolerant population.
Highlights
HIV/AIDS has been one of the most deadly diseases around the world since the first patients were documented in 1981
Anderson et al [2] investigated the dynamics of the initial HIV models using ordinary differential equations. e models have been improved by adding into various factors on the disease [3,4,5]
The research works on the switched HIV/AIDS epidemic models are very few [36,37,38]. is paper has studied the global asymptotical stability of new fractional order HIV/AIDS models with switching parameters and treatment compartment
Summary
HIV/AIDS has been one of the most deadly diseases around the world since the first patients were documented in 1981. Silva and Torres [8] introduced the fractional order into an HIV/AIDS model and surveyed local and uniform stability of its disease-free equilibrium. Modelling the dynamical behavior of the epidemic diseases by fractional derivative models has more effective than interorder modelling [13,14,15]. Is paper mainly develops and investigates switched HIV/AIDS models with drug treatment involving Caputofractional derivatives. The models’ parameters under the influence of seasonality are supposed to be varying in time and change their function forms, and the derivative of the model is assumed to be fractional order with its memory property, which leads to a novel HIV/AIDS model.
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